<PRE><B>Question 1210570</B>
.
Let P_1 P_2 P_3 ... P_{10} be a regular polygon inscribed in a circle with radius 1.  Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + . . .  + P_9 P_{10} + P_{10} P_1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



If this sum 


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;P_1 P_2 + P_2 P_3 + P_3 P_4 + . . .  + P_9 P_{10} + P_{10} P_1


is the sum of vectors, then this sum is equal to zero - as any sum of vectors along a closed contour.



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